Analysis and prediction of the packing of α-helices against a β-sheet in the tertiary structure of globular proteins

The packing of α-helices and β-sheets in six αβ proteins (e.g. flavodoxin) has been analysed. The results provide the basis for a computer algorithm to predict the tertiary structure of an αβ protein from its amino acid sequence and actual assignment of secondary structure. The packing of an individual α-helix against a β-sheet generally involves two adjacent ± 4 rows of non-polar residues on the α-helix at the positions i, i + 4, i + 8, i + 1, i + 5, i + 9. The pattern of interacting β-sheet residues results from the twisted nature of the sheet surface and the attendant rotation of the side-chains. At a more detailed level, four of the α-helical residues (i + 1, i + 4, i + 5 and i + 8) form a diamond that surrounds one particular β-sheet residue, generally isoleucine, leucine or valine. In general, the α-helix sits 10 A above the sheet and lies parallel to the strand direction. The prediction follows a combinational approach. First, a list of possible β-sheet structures (106 to 1014) is constructed by the generation of all β-sheet topologies and β-strand alignments. This list is reduced by constraints on topology and the location of non-polar residues to mediate the sheet/helix packing, and then rank-ordered on the extent of hydrogen bonding. This algorithm was uniformly applied to 16 αβ domains in 13 proteins. For every structure, one member of the reduced list was close to the crystal structure; the root-mean-square deviation between equivalenced Cα atoms averaged 5.6 A for 100 residues. For the αβ proteins with pure parallel β-sheets, the total number of structures comparable to or better than the native in terms of hydrogen bonds was between 1 and 148. For proteins with mixed β-sheets, the worst case is glyceraldehyde-3-phosphate dehydrogenase, where as many as 3800 structures would have to be sampled. The evolutionary significance of these results as well as the potential use of a combinatorial approach to the protein folding problem are discussed.